Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 6R + 9C s.t. R + 3 2C ≤ 1,000 Cutting and sewing 1 2R + 1 3C ≤ 300 Finishing 1 8R + 1 4C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHS Value Allowable Increase Allowable Decrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3 100.00000 55.00000 25.00000 (a) What is the optimal solution, and what is the value of the total profit contribution? regular glove -- catcher's mitt -- value -- (b) Which constraints are binding? (Select all that apply.) cutting and sewing finishing packaging and shipping (c) What are the dual values for the resources? Interpret each. constraint 1 Each additional hour of cutting and sewing will improve profits by $4.50 or Each additional hour of cutting and sewing will improve profits by $275.00 or Each additional hour of cutting and sewing will improve profits by $30.00 or Additional hours of cutting and sewing will not improve profits. constraint 2 Each additional hour of finishing will improve profits by $4.50 or Each additional hour of finishing will improve profits by $275.00 or Each additional hour of finishing will improve profits by $30.00 or Additional hours of finishing will not improve profits. constraint 3 Each additional hour of packing and shipping will improve profits by $4.50 or Each additional hour of packing and shipping will improve profits by $275.00 or Each additional hour of packing and shipping will improve profits by $30.00 or Additional hours of packing and shipping will not improve profits. (d) If overtime can be scheduled in one of the departments, where would you recommend doing so? cutting and sewing or finishing or packaging and shipping

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 6R + 9C s.t. R + 3 2C ≤ 1,000 Cutting and sewing 1 2R + 1 3C ≤ 300 Finishing 1 8R + 1 4C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHS Value Allowable Increase Allowable Decrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3 100.00000 55.00000 25.00000 (a) What is the optimal solution, and what is the value of the total profit contribution? regular glove -- catcher's mitt -- value -- (b) Which constraints are binding? (Select all that apply.) cutting and sewing finishing packaging and shipping (c) What are the dual values for the resources? Interpret each. constraint 1 Each additional hour of cutting and sewing will improve profits by $4.50 or Each additional hour of cutting and sewing will improve profits by $275.00 or Each additional hour of cutting and sewing will improve profits by $30.00 or Additional hours of cutting and sewing will not improve profits. constraint 2 Each additional hour of finishing will improve profits by $4.50 or Each additional hour of finishing will improve profits by $275.00 or Each additional hour of finishing will improve profits by $30.00 or Additional hours of finishing will not improve profits. constraint 3 Each additional hour of packing and shipping will improve profits by $4.50 or Each additional hour of packing and shipping will improve profits by $275.00 or Each additional hour of packing and shipping will improve profits by $30.00 or Additional hours of packing and shipping will not improve profits. (d) If overtime can be scheduled in one of the departments, where would you recommend doing so? cutting and sewing or finishing or packaging and shipping

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section: Chapter Questions

Problem 1C

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Question

100%

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting

R = number of regular gloves
C = number of catcher's mitts

leads to the following formulation:

Max

s.t.

≤

1,000

Cutting and sewing

≤

300

Finishing

≤

100

Packaging and shipping

≥ 0

The computer solution is shown below.

Optimal Objective Value = 4350.00000

Variable	Value	Reduced Cost
R	500.00000	0.00000
C	150.00000	0.00000

Constraint	Slack/Surplus	Dual Value
1	275.00000	0.00000
2	0.00000	4.50000
3	0.00000	30.00000

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
R	6.00000	7.50000	1.50000
C	9.00000	3.00000	5.00000

Constraint	RHS Value	Allowable Increase	Allowable Decrease
1	1000.00000	Infinite	275.00000
2	300.00000	100.00000	166.66667
3	100.00000	55.00000	25.00000

(a)

What is the optimal solution, and what is the value of the total profit contribution?

regular glove --

catcher's mitt --

value --

(b)

Which constraints are binding? (Select all that apply.)

cutting and sewing

finishing

packaging and shipping

(c)

What are the dual values for the resources? Interpret each.

constraint 1

Each additional hour of cutting and sewing will improve profits by $4.50

Each additional hour of cutting and sewing will improve profits by $275.00

Each additional hour of cutting and sewing will improve profits by $30.00

Additional hours of cutting and sewing will not improve profits.

constraint 2

Each additional hour of finishing will improve profits by $4.50

Each additional hour of finishing will improve profits by $275.00

Each additional hour of finishing will improve profits by $30.00

Additional hours of finishing will not improve profits.

constraint 3

Each additional hour of packing and shipping will improve profits by $4.50

Each additional hour of packing and shipping will improve profits by $275.00

Each additional hour of packing and shipping will improve profits by $30.00

Additional hours of packing and shipping will not improve profits.

(d)

If overtime can be scheduled in one of the departments, where would you recommend doing so?

cutting and sewing or

finishing or

packaging and shipping

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